We study the contracting problem in the persistent private information model of Williams [17], in which an agent provides a report of a privately observed path to the principal, who in turn pays the agent in the least expensive way that induces truthful reporting. We first argue that, in the case of persistent information, the contract in [17] does not induce truthful reporting if misreporting is allowed to grow sufficiently fast. The contract becomes incentive compatible (i.e., induces truthful reporting) if one imposes additional restrictions on misreporting, as shown also in Bloedel, Krishna, and Strulovici [2] under conditions different from ours. Under such restrictions, we show that the contract identified in [2] is optimal among linear contracts. On the other hand, if additional restrictions are not imposed, we show that the contract optimal in a family of generalized linear contracts is deterministic.
